Summary: Forcing Monotonicity in Parameterized
Verification: From Multisets to Words
Parosh Aziz Abdulla
Uppsala University
Department of Information Technology
P.O. Box 337
751 05 Uppsala
Sweden
http://user.it.uu.se/ parosh/
Abstract. We present a tutorial on verification of safety properties for
parameterized systems. Such a system consists of an arbitrary number of
processes; the aim is to prove correctness of the system regardless of the
number of processes inside the system. First, we consider a class of pa-
rameterized systems whose behaviours can be captured exactly as Petri
nets using counter abstraction. This allows analysis using the framework
of monotonic transition systems introduced in [1]. Then, we consider pa-
rameterized systems for which there is no natural ordering which allows
monotonicity. We describe the method of monotonic abstraction which
provides an over-approximation of the transition system. We consider
both systems where the over-approximation gives rise to reset Petri nets,